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Given binomial coefficient (N; k), write N-k+i=a_ib_i, for 1<=i<=k, where b_i contains only those prime factors >k. Then the number of i for which b_i=1 (i.e., for which all ...

The operation of drilling a tubular neighborhood of a knot K in S^3 and then gluing in a solid torus so that its meridian curve goes to a (p,q)-curve on the torus boundary of ...

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...

A.k.a. the pigeonhole principle. Given n boxes and m>n objects, at least one box must contain more than one object. This statement has important applications in number theory ...

A doublecross graph is a graph with graph crossing number 2. The numbers of doublecross simple graphs on n=1 nodes are 0, 0, 0, 0, 0, 1, 39, ..., and the numbers of connected ...

The dual of a regular tessellation is formed by taking the center of each polygon as a vertex and joining the centers of adjacent polygons. The triangular and hexagonal ...

A number n is called an economical number if the number of digits in the prime factorization of n (including powers) uses fewer digits than the number of digits in n. The ...

In mathematics, a small positive infinitesimal quantity, usually denoted epsilon or epsilon, whose limit is usually taken as epsilon->0. The late mathematician P. Erdős also ...

A mathematical structure first introduced by Kolyvagin (1990) and defined as follows. Let T be a finite-dimensional p-adic representation of the Galois group of a number ...

An even permutation is a permutation obtainable from an even number of two-element swaps, i.e., a permutation with permutation symbol equal to +1. For initial set {1,2,3,4}, ...